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Simplifying 4x2 + 28x + 58 = 0 Reorder the terms: 58 + 28x + 4x2 = 0 Solving 58 + 28x + 4x2 = 0 Solving for variable 'x'. Factor out the Greatest Common Factor (GCF), '2'. 2(29 + 14x + 2x2) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(29 + 14x + 2x2)' equal to zero and attempt to solve: Simplifying 29 + 14x + 2x2 = 0 Solving 29 + 14x + 2x2 = 0 Begin completing the square. Divide all terms by 2 the coefficient of the squared term: Divide each side by '2'. 14.5 + 7x + x2 = 0 Move the constant term to the right: Add '-14.5' to each side of the equation. 14.5 + 7x + -14.5 + x2 = 0 + -14.5 Reorder the terms: 14.5 + -14.5 + 7x + x2 = 0 + -14.5 Combine like terms: 14.5 + -14.5 = 0.0 0.0 + 7x + x2 = 0 + -14.5 7x + x2 = 0 + -14.5 Combine like terms: 0 + -14.5 = -14.5 7x + x2 = -14.5 The x term is 7x. Take half its coefficient (3.5). Square it (12.25) and add it to both sides. Add '12.25' to each side of the equation. 7x + 12.25 + x2 = -14.5 + 12.25 Reorder the terms: 12.25 + 7x + x2 = -14.5 + 12.25 Combine like terms: -14.5 + 12.25 = -2.25 12.25 + 7x + x2 = -2.25 Factor a perfect square on the left side: (x + 3.5)(x + 3.5) = -2.25 Can't calculate square root of the right side. The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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